1. Field of the Invention
The present invention relates to a positioning apparatus installed on a semiconductor exposure apparatus, a liquid crystal exposure apparatus, a measuring apparatus, and a processing apparatus.
2. Description of the Related Art
A wafer stage and a reticle stage used for the exposure apparatus requires high positioning accuracy to correctly transfer microscopic circuit patterns. Therefore, a stage position control system requires a high control band.
The stage position control system also requires high acceleration and high-speed movement to improve the productivity. Although an actuator having a large thrust is used to meet the above-mentioned requirements, the use of such an actuator may increase heat generation therein, possibly resulting in degradation in positioning accuracy. Accordingly, weight reduction of the stages is to be done to reduce the required thrust. However, since weight reduction of the stages decreases an eigenvalue of the elastic vibration mode of the stage structure, gain and phase margins of the position control system decrease and oscillation of the elastic vibration mode becomes likely to occur, thus making it difficult to improve the control band.
Japanese Patent Application Laid-Open No. 2005-150615 discusses a stage configuration for achieving a high control band by using a stage having a low eigenvalue. With this configuration, Z actuators are arranged at nodes of the elastic vibration mode of the stage or at positions where vibrations are mutually negated, resulting in distribution of the thrust. Thus, a high control band can be achieved without being affected by low-order elastic vibration modes.
Japanese Patent Application Laid-Open No. 2008-300828 also discusses a configuration for distributing the thrust to four Z actuators not to cause excitation of the first-order torsional mode. With the conventional techniques, the arrangement of actuators and the thrust distribution ratio for each actuator are determined on the assumption that the deformation shape of the elastic vibration mode is known. Although the deformation shape of the elastic vibration mode can be obtained by using finite element method (FEM) simulation, the deformation shape obtained by the simulation does not completely agree with the deformation shape measured on a real apparatus, resulting in an error. There is also an error in actuator arrangement between design values and the real apparatus because of a manufacture error. Therefore, even when the actuator arrangement and the thrust distribution ratio are determined based on a simulation result or design values, there maybe a situation that the effect of the elastic vibration mode cannot be effectively reduced.
Meanwhile, modal analysis is one of techniques for measuring the deformation shape of the elastic vibration mode of a real apparatus, with which vibration excited by an impact hammer is measured by an accelerometer. This technique requires time and effort and provides a low measurement accuracy making it difficult to accurately measure the deformation shape at actuator positions. Therefore, improving the measurement accuracy is difficult even when the thrust distribution ratio is determined based on the deformation shape measured on the real apparatus. The conventional techniques have not discussed a method for adjusting thrust distribution on the real apparatus when the deformation shape cannot be correctly obtained. Since there has been no choice other than manually repeating trial and error, the conventional techniques require time and effort but do not guarantee the improvement in performance as a result of thrust distribution adjustment.